Subtract 7x^2−5xy+8y^2 from −2x^2−15xy+9y^2

Step-by-step explanation:

We want to subtract from .

We set up the subtraction problem as follows:

.

We expand the brackets to obtain;

.

We regroup the terms to obtain;

.

We now simplify to obtain;

.

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4